Calculating the market risk premiumbeta and required rate of return. CAPM. Portfolio Risk &Return.

We have a portfolio of threepositively correlated but not perfectly correlated stocks.

(Correlation co-efficient between0-1)

Stock Expected Rate ofReturn StandardDeviation Beta

X 10% 16% .75

Y 12% 16% 1.25

Z 13% 16% 1.50

What is the market risk premium forthe portfolio ?

Required Rate of Return For the Stock= Risk Free rate of Return +

+ ( Market Risk Premium * Beta ofstock )

Market Risk Premium = Market Required Rate of Return – Risk Free rate of Return

The returns on stocks X, Y and Z andtheir beta have been provided. Using the information provided, wewill first calculate the market risk premium.

The capital asset pricing model is amodel based on the proposition that any stock's required rate ofreturn is equal to the risk free rate of return plus a risk premiumthat reflects only the risk remaining after diversification.

The required rate of return for astock is calculated by adding the risk free rate of return to theproduct of the market risk premium and the stock's beta.

The market risk premium shows thepremium that investors require for bearing the risk of averagestock and is calculated by deducting the risk free rate from themarket's required rate of return.

Now, using stock X or any other stock,we can calculate the market risk premium. We'll use stock X. Theexpected return on this stock is 10%. The risk free rate is 7&and the stock's beta is .75.

By solving the equation we determinethe market risk premium to be 4%.

Next, we will calculate the beta ofFund Q.

Fund Q has 1/3 of its funds investedin each of the three stocks X, Y, and Z.

Thus, the beta of Fund Q will be thesum of one third of the beta of each stock. One third of .75 is.25. One third of 1.25 is .4167 and one third of 1.5 is .5. Byadding .25, .4167 and .5, we calculate the beta of Fund Q as1.1667.

Let’s now calculate the requiredreturn of Fund Q. The risk free rate is 7%. The market risk premiumis calculated to be 4%. The beta of Fund Q is 1.1667. By adding 7%to the product of 4% and 1.1667, we determine the required returnon Fund Q to be 11.67%.

Since the returns on the three stocks included in Fund Q are notpositively correlated, the standard deviation of the fund will beless than 16%.